The magneto-elastica: from self-buckling to self-assembly

D. Vella, E. du Pontavice, C. L. Hall, A. Goriely

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


Spherical neodymium-iron-boron magnets are permanent magnets that can be assembled into a variety of structures owing to their high magnetic strength. A one-dimensional chain of these magnets responds to mechanical loadings in a manner reminiscent of an elastic rod. We investigate the macroscopic mechanical properties of assemblies of ferromagnetic spheres by considering chains, rings and chiral cylinders of magnets. Based on energy estimates and simple experiments, we introduce an effective magnetic bending stiffness for a chain of magnets and show that, used in conjunction with classic results for elastic rods, it provides excellent estimates for the buckling and vibration dynamics of magnetic chains. We then use this estimate to understand the dynamic self-assembly of a cylinder from an initially straight chain of magnets.
Original languageEnglish (US)
Pages (from-to)20130609
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2162
StatePublished - Dec 4 2013
Externally publishedYes


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